Question

Express the following decimal as a rational number.

17.027

Answer 1

Let x = 17.027
= 17.027777..
Here, only number 7 is being repeated, so first we need to remove 02 which proceeds 7.
We multiply by 100 so that only the recurring digits remain after decimal.
∴ 100x = 1702.7777....       ....(1)
The number of digits recurring in equation (1) is 1, so we multiply both sides of the equation (1) by 10.
∴ 1000x = 10 x 1702.7777....
= 17027.7774.....        ....(2)
On subtracting (1) from (2), we get
900x = 15325

∴ x = `(15325)/(900)`

= `(613)/(26)`

∴ 17.027 = `(613)/(36)`